..in theory, the insurance company could invest the lump sum in fixed interest securities at the start of the contract, choosing a spread of redemption dates such that the redemption amounts being paid each year are exactly equal to the amount by which the fund needs to be disinvested in that year. This was the line written in Book Chapter 3 under Investment risk of Annuities Can anyone help with it
I think what the reading here suggests is that the lump sum could be invested in a variety of bonds with different redemption dates. With each bond purchased comes with its own set of coupon payments, and the redemption amount paid upon maturity (i.e. the return of the principal). So in a way, the redemption amount mimics the disinvestment component of an annuity's pay out mechanism. (In the earlier reading, it mentions that a combination of both the income earned on the lump sum investment and a portion of the lump sum disinvested is needed to support the payments of the annuity.) Hope my understanding is correct.
Thanks for answering this one Nicholas - that's exactly right. A numerical example might help. Assume that the annuity payments at the end of each year are 444, 428, 212, 104. Assume also that bonds pay 100 on redemption plus an annual coupon of 4. We can match these annuities with 4 one-year bonds (416), 4 two-year bonds (16, 416), 2 three-year bonds (8, 8, 208) and 1 four-year bond (4, 4, 4, 104). So the coupons and redemption proceeds with bonds are various terms can match the annuity payments. Best wishes Mark
